Specific emitter identification using histogram of oriented gradient features

ABSTRACT

In one embodiment, a method for specific emitter identification includes receiving a signal from an emitter indicative of a hardware characteristic of the emitter. A computer-readable representation of the received signal is generated. A plurality of gradients for each partition of a plurality of partitions of the computer-readable representation is computed. Each gradient is indicative of at least the angular orientation of a respective portion of the computer-readable representation. A histogram is computed for each partition by assigning each computed gradient to a bin based at least in part on the magnitude of the computed gradient. One or more Histogram of Oriented Gradient (HOG) features are extracted from a concatenation of the bins of all of the computed histograms. The one or more HOG features are compared to one or more corresponding HOG features stored on a computer-readable medium. Based at least in part on the comparison, a determination is made regarding whether the emitter has a particular identification.

TECHNICAL FIELD

This disclosure relates in general to specific emitter identification,and more particularly to a specific emitter identification usinghistogram of oriented gradient features.

BACKGROUND

Histogram of Oriented Gradient descriptors, or HOG descriptors, arefeature descriptors used in computer vision and image processing for thepurpose of object detection. Algorithms associated with HOG descriptorshave been used to identify or otherwise distinguish particular featuresof a static image or video from the background. For example, HOGdescriptors have been used to identify a particular vehicle in asatellite image. Additionally, HOG descriptors have been used todistinguish a human profile from the background of a photograph.

Specific emitter identification (SEI) typically involves accuratelymeasuring and storing signal features that are consistent from onetransmission to another for a given emitter, but differ from emitter toemitter. A particular emitter may then be identified by attempting tomatch measured emissions with previously stored emissions. ConventionSEI matching methods are limited for a variety of reasons.

SUMMARY

In one embodiment, a method for specific emitter identification includesreceiving a signal from an emitter indicative of a hardwarecharacteristic of the emitter. A computer-readable representation of thereceived signal is generated. A plurality of gradients for eachpartition of a plurality of partitions of the computer-readablerepresentation is computed. Each gradient is indicative of at least theangular orientation of a respective portion of the computer-readablerepresentation. A histogram is computed for each partition by assigningeach computed gradient to a bin based at least in part on the magnitudeof the computed gradient. One or more Histogram of Oriented Gradient(HOG) features are extracted from a concatenation of the bins of all ofthe computed histograms. The one or more HOG features are compared toone or more corresponding HOG features stored on a computer-readablemedium. Based at least in part on the comparison, a determination ismade regarding whether the emitter has a particular identification.

Technical advantages of certain embodiments of the present disclosureinclude simple, fast, and robust methods for specific radio frequencyemitter identification. Various embodiments may identify or“fingerprint” individual transmitters based solely on their hardwarecharacteristics in a manner that is completely independent of atransmitted message. Some methods may reliably identify particularemitters that produce slightly inconsistent emission patterns. Some suchmethods can reliably identify such transmitters with only a singlerecorded emission. In some embodiments, more difficult transmitters withvariable signatures can be reliably fingerprinted by recording severalturn-on transients using Histograms of Oriented Gradient (HOG) features.

Other technical advantages of the present disclosure will be readilyapparent to one skilled in the art from the following figures,descriptions, and claims. Moreover, while specific advantages have beenenumerated above, various embodiments may include all, some, or none ofthe enumerated advantages.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of the present disclosure and itsadvantages, reference is now made to the following description, taken inconjunction with the accompanying drawings, in which:

FIG. 1 is a portion of an emitter identification system according to oneembodiment;

FIG. 2 is a flowchart illustrating an example method for generating acomputer-readable representation of an electromagnetic emission that maybe used by the system of FIG. 1 according to one embodiment;

FIGS. 3A through 3D illustrate respective example graphicalrepresentations that may be generated and/or used by the system of FIG.1 for specific emitter identification according to one embodiment; and

FIG. 4 is a flowchart illustrating an example method for specificemitter identification that may be used by the system of FIG. 1according to one embodiment.

DETAILED DESCRIPTION

Particular embodiments of the present disclosure may be used in thecontext of fingerprinting and identifying individual radio frequency(RF) transmitters based on their time-frequency turn-on characteristics.In some embodiments, a spectrogram of the turn-on transient is analyzedusing Histograms of Oriented Gradient (HOG) features. The degree ofsimilarity between a stored template HOG features and the HOG featurescalculated from the transient spectrogram of an emitter may be used toidentify the individual emitter. The example embodiments of the presentdisclosure are best understood by referring to FIGS. 1 through 3 of thedrawings, like numerals being used for like and corresponding parts ofthe various drawings.

FIG. 1 is a block diagram of a portion of an emitter identificationsystem 100 according to one embodiment. In this example, system 100generally includes a receiver 102 capable of receiving a signal 103 froman emitter 104, an amplifier 106, a signal processor 108, a scope 110, aclient 112, and a database 111. In general, scope 110 generates acomputer-readable representation of an amplified and modulated inputsignal received from emitter 104. A Specific Emitter Identification(SEI) application 116 residing in storage 118 of client 112 may use thecomputer-readable representation to identify or “fingerprint” individualemitters 104, as explained further below.

Emitter 104 generally refers to any device capable of emitting anelectromagnetic signal 103. For example, emitter 104 may be a radiotransmitter, a garage door opener, a key fob, a transponder, a cellularphone, a cordless phone, a computer (e.g., a handheld computer, a laptopcomputer, a desktop computer etc.), or any other device capable ofemitting an electromagnetic signal. In this example, emitter 104 is acellular telephone capable of generating radio frequency signals 103that may be received by receiver 102. Receiver 102 generally refers toany device capable of receiving an electromagnetic signal 103 fromemitter 104. In this example, receiver 102 is a radio frequency (RF)receiver that communicates the received signal 103 to amplifier 106.

Amplifier 106 generally converts a received input signal 103 (e.g., onewith a very small amount of energy, which may be a few milliwatts in oneexample) into a different output signal (e.g., one with a larger amountof energy than the input signal). In this example, amplifier 106amplifies the signal received from receiver 102 and communicates theamplified signal to signal processor 108; however, some alternativeembodiments may not include signal processor 108. Signal processor 108generally refers to any component(s) capable of processing an inputsignal to produce an output signal that may be used by scope 110. Forexample, signal processor 108 may include one or more mixers, signalgenerators, electronic filters, analog-to-digital (A/D) converters, anycombination of the preceding, or some other device capable of processingan input signal to produce an output that may be used by scope 110.

Scope 110 generally refers to any suitable device(s) capable ofgenerating a computer-readable representation of an input signal (e.g.,the digitization of respective input signals used to generate thespectrograms 300, 310, 320, and 330 illustrated in FIGS. 2A through 2D).In this example, scope 110 includes an analog-to-digital (A/D) converterthat may sample an analog input, received from signal processor 108, atspeeds up to 500 MS/s (i.e. a new sample may be taken every twonanoseconds); however, scope 110 may use alternative configurations(e.g., slower or faster sampling rates of an input signal) to generate acomputer-readable representation from any of a variety of input signals(e.g., a digital input signal digitized by signal processor 108).According to one embodiment of the present disclosure, scope 110 may bea CompuScope 8500 of Gage Applied Technologies. In this example, scope110 communicates the computer-readable representation of the inputsignal to client 112 and/or database 111.

Database 111 generally stores data, and facilitates addition,modification, and retrieval of such data. In various embodiments,database 111 may be used to conveniently consolidate allcomputer-readable representations generated by scope 111 and/orprocessed by client 112. In this example, database 111 resides separatefrom scope 110 and client 112. For example, database 111 may be storedon a separate dedicated server. In other embodiments, however, database111 may alternatively reside, for example, within scope 110 or client112.

Client 112 generally refers to any suitable device(s), applications,other logic, or a combination of any of the preceding capable of using acomputer-readable representation of an input signal toidentify/fingerprint the particular emitter 104 associated with theinput signal. For example, client 112 may include a personal digitalassistant, a computer (e.g., a laptop, a desktop, a server, or any othersuitable computer), a cellular telephone, a mobile handset, or any otherdevice capable of using a computer-readable representation of an inputsignal to identify/fingerprint the particular emitter 104 associatedwith the input signal. Logic as used herein generally performs theoperations of a particular component, such as executing instructions togenerate output from input. Logic may include hardware, software, otherlogic, or a combination of any of the preceding. In some embodiments,logic associated with client 112 may manage the operation of a componentof system 100. In this example, client 112 includes a processor 114, astorage device 116, an input device 118, an output device 120,communication interface 122, and a memory device 124. The components114-124 of client 112 may be coupled to each other in any suitablemanner. In the illustrated embodiment, the components 114-124 of client112 are coupled to each other by a bus.

Processor 114 generally refers to any suitable device capable ofexecuting instructions and manipulating data to perform operations forclient 112. For example, processor 114 may include any type of centralprocessing unit (CPU). Input device 118 may refer to any suitable devicecapable of inputting, selecting, and/or manipulating various data andinformation. For example, input device 118 may include a keyboard,mouse, graphics tablet, joystick, light pen, microphone, scanner, orother suitable input device. Memory device 124 may refer to any suitabledevice capable of storing and facilitating retrieval of data. Forexample, memory device 124 may include random access memory (RAM), readonly memory (ROM), a magnetic disk, a disk drive, a compact disk (CD)drive, a digital video disk (DVD) drive, removable media storage, or anyother suitable data storage medium, including combinations thereof.

Communication interface 122 may refer to any suitable device capable ofreceiving input for client 112, sending output from client 112,performing suitable processing of the input or output or both,communicating to other devices, or any combination of the preceding. Forexample, communication interface 122 may include appropriate hardware(e.g., modem, network interface card, etc.) and software, includingprotocol conversion and data processing capabilities, to communicatethrough a LAN, WAN, or other communication system that allows client 112to communicate to other devices. Communication interface 122 may includeone or more ports, conversion software, or both. Output device 120 mayrefer to any suitable device capable of displaying information to auser. For example, output device 120 may include a video/graphicaldisplay, a printer, a plotter, or other suitable output device.

Storage device 116 may refer to any suitable device capable of storingcomputer-readable data and instructions. Storage device 116 may include,for example, logic in the form of software applications, computer memory(e.g., Random Access Memory (RAM) or Read Only Memory (ROM)), massstorage media (e.g., a magnetic drive, a disk drive, or optical disk),removable storage media (e.g., a Compact Disk (CD), a Digital Video Disk(DVD), or flash memory), a database and/or network storage (e.g., aserver), other computer-readable medium, or a combination and/ormultiples of any of the preceding. In this example, an SEI application150 embodied as logic within storage 112 generally manages acts used toidentify/fingerprint the computer-readable signal representationsgenerated by scope 110; however, SEI application 150 may alternativelyreside within any of a variety of other suitable computer-readablemedium, including, for example, memory device 124, database 111,removable storage media (e.g., a Compact Disk (CD), a Digital Video Disk(DVD), or flash memory), any combination of the preceding, or some othercomputer-readable medium.

The components 102, 104, 106, 108, 110, 112, and 114 of system 100 maybe integrated or separated. Although FIG. 1 provides one example ofcomputer-readable storage 112 as operating separate from scope 110, inother embodiments storage 112 may operate within scope 110. In someembodiments, components 102, 106, 108, 110 and 114 may each be housedwithin a single chassis. As used in this document, “each” refers to eachmember of a set or each member of a subset of a set. The operations ofsystem 100 may be performed by more, fewer, or other components. Forexample, the operations of amplifier 106 and signal processor 108 may beperformed by one component, or the operations of scope 110 may beperformed by more than one component. Additionally, operations of system100 may be performed using any suitable logic that may comprisesoftware, hardware, other logic, or any suitable combination of thepreceding. The general operation of system 100 and example acts that maybe managed and/or executed by SEI application 150 are described furtherbelow with reference to FIGS. 2 through 4.

FIG. 2 is a flowchart 300 illustrating an example method for generatinga computer-readable representation of an electromagnetic emission 103that may be used by system 100 according to one embodiment. In thisexample, system 100 generally generates one or more two-dimensionalrepresentations (e.g., spectrograms) of emission 103 in thetime-frequency domain based on the turn-on characteristics ofcorresponding emitters 104; however, any suitable computer-readablerepresentation may be used. For example, some alternativerepresentations may include, but are not limited to, Wigner andGabor-Wigner distributions corresponding to emission 103.

In this example, receiver 102 receives a uniquely identifiableelectromagnetic signal 103 from emitter 104 in act 202. For example,receiver 102 may capture a turn-on transient emitted by emitter 104.Turn-on transients typically contain signal features unique to theactual hardware of a corresponding emitter 104 (i.e. independent of anyinformation encoded in the transmission) and thus may provide a uniquelyidentifiable fingerprint for each emitter 104. That is, the turn-ontransient signal features are typically consistent from one transmissionto another for a given emitter 104, but differ from emitter to emitter.In some embodiments, even emitters 104 of the same make and model mayeach produce a uniquely identifiable turn-on transient.

The received signal 103 is processed in act 204. Such processing may ormay not include converting the received electromagnetic signal 103 intoelectrical form, amplifying the signal by amplifier 106, mixing thesignal with another signal generated by a signal generator (notexplicitly shown), electrically filtering the signal, converting theelectrical signal (e.g., analog-to-digital conversion) any combinationof the preceding, or any of a variety of other signal processing acts.In various embodiments, the signal processing of act 204 may be effectedby signal processor 108. In this example, however, scope 110 performs atleast some of the signal processing by executing an analog-to-digitalconversion of the signal in act 206. A computer-readable representationof the digitized signal is generated in act 208. In this example, scope110 generates data, in act 208, which may be used to construct atwo-dimensional spectrogram of the turn-on transient in thetime-frequency domain. In act 210, the spectrogram data is stored, forexample, in storage 116, memory 124, database 111, any combination ofthe proceeding, or some other suitable computer-readable medium. SEIapplication 150 may use the stored spectrogram data to extract HOGfeatures for specific emitter identification. The degree of similaritybetween a template of stored HOG features and the HOG features extractedfrom the turn-on transient spectrogram of emitter 104 may then be usedto identify the particular emitter 104.

FIGS. 3A through 3D illustrate example spectrograms 300, 310, 320, and330, respectively, which may be generated and/or used by system 100 forspecific emitter identification (SEI) according to one embodiment. Eachspectrogram 300, 310, 320, and 330 captures one or more uniquecharacteristics of a respective emitter 104, thereby providing anidentifiable fingerprint for the emitter 104. In this example, emitters104 are identified by capturing respective turn-on transients in thetime-frequency domain; however, any suitable analysis of anyidentifiable signal may be used. The spectrogram of the turn-ontransient of an RF emitter 104 may be represented as

$\begin{matrix}{{S\left( {t,f} \right)} = {{\int_{- \infty}^{\infty}{{h^{*}\left( {u - t} \right)}{s(u)}{\mathbb{e}}^{{- {j2}}\;\pi\;{fu}}\ {\mathbb{d}u}}}}^{2}} & {{Equation}\mspace{14mu} 1}\end{matrix}$where s(t) is the signal and h(t) is a window function. Equation 1 maybe used to obtain the time-frequency distribution of the turn-ontransient of any given emitter 104.

In this example, FIGS. 3A and 3B illustrate first and second actualrecordings of the turn-on transient for a first emitter 104; and FIGS.3C and 3D illustrate first and second actual recordings of the turn ontransient for a second emitter 104 of the same make and model. Repeatedrecordings of the turn-on emissions showed that some variation may existeven for the same transmitter. Therefore, a brittle matching method suchas two-dimensional correlation may not be robust enough for someapplications. Accordingly, some embodiments of the present disclosurerecognize a method for specific emitter identification based at least inpart on the HOG features of a spectrogram. An example method forspecific emitter identification using HOG features of a spectrogram aredescribed further with reference to FIG. 4.

FIG. 4 is a flowchart 400 illustrating an example method for specificemitter identification that may be used by system 100 according to oneembodiment. In general, the HOG features of an emission's spectrogrammay be used to extract identifying information of the emission's source.That is, the HOG features are determined from a graphical representationof signal patterns emitted by a particular emitter 104. This exampleuses the time-frequency distributions of spectrograms captured from theturn-on transient of emitter 104 (e.g., spectrograms 300, 310, 320 and330 illustrated in FIGS. 3A through 3D, respectively); however, anysuitable computer-readable representation that captures any suitablesignal component may be used (e.g., computer-readable representationsthat capture signal components that include amplitude, phase, three ormore dimensions, etc.).

In act 402, a computer-readable representation of an input signal isseparated into partitions. For example, data that may be displayed as atwo-dimensional representation of the input signal may be analyticallydivided into a grid of cells. In some embodiments, it may not benecessary to analyze the features of every cell. For example, it may beadvantageous to select for processing only those cells with significantsignal energy in order to reduce computational complexity and improveaccuracy. Act 402 may thus additionally involve selecting the particularcells to process.

In act 404, a gradient operator is used on at least a subset of thecells (e.g., the cells selected in act 402) in order to estimate theangular orientation and gradient strength of edges in the cell.According to one embodiment, the gradient operator involves convolutionwith a Sobel kernel. In act 406, a weighted orientation histogram iscalculated. For example, the contribution of each time-frequency datapoint may be assigned to a histogram orientation bin by the strength ormagnitude of the gradient at that location.

In act 408, the histogram of each cell may then be normalized using, forexample, the sum of all histogram bins in a block of cells centered onthe cell being processed. If the cells are equal-sized squares,rectangles or diamonds, for example, a particular cell may be normalizedusing the sum of eight neighboring cells that share a common “side” withthe particular cell. Thus, in some embodiments, the same cell or blockof cells may be used more than once during the normalization of act 408.In other words, the neighboring cells used to normalize one particularcell may overlap with the neighboring cells used to normalize anotherparticular cell. In this manner, act 408 may help to make the featuresmore robust against contrast variations.

A resulting HOG feature vector is determined in act 410 by concatenatingall of the histogram bins for all of the applicable cells (e.g., thecells selected in act 402). Act 412 involves computing the distancebetween the determined HOG feature vectors and the stored featurevectors of previously recorded emissions (e.g., feature vectors that maybe stored within database 111, storage 112, or some other suitablecomputer-readable medium). For example, the K-Nearest-Neighbor (KNN)algorithm can be used to compensate for variability between signals bycomparing the input signal to multiple examples of stored signalsignatures.

A decision is made in act 414 regarding whether the computed differencebetween the closest recorded features and the determined HOG featurevectors is less than a predetermined threshold. If the distance is lessthan the threshold, a match to the stored signal data is found and theidentity of a particular emitter is confirmed in act 416. If thedifference is greater than the predetermined threshold, then theconclusion in act 418 is that no match exists. Flowchart 400 ends aftercompleting either act 416 or 418.

Thus, various embodiments provide a simple, fast, and robust method forspecific emitter identification. Various embodiments may identify orfingerprint individual transmitters based solely on their hardwarecharacteristics in a manner that is completely independent of atransmitted message. Such hardware characteristics provide an electronicfingerprint that is difficult, if not impossible, to imitate orcounterfeit. For example, the turn-on transient of an emitter maysignificantly differ even between the same models of a particular devicemade by the same manufacture using precisely the same components.

Additional example applications of the present disclosure includesecurity applications in wireless networks where intruders or legitimateusers could be identified based on physical hardware characteristics,home security features (e.g., garage door openers), toll road or parkinggarage transponder systems, and so forth. In addition, the disclosure ofthe present invention may be used in surveillance applications. Forexample, the recordings over time of various emissions in a particulararea may later be used to identify a particular emission source. Such afeature may be useful, for example, to identify a particular device usedto trigger an explosion.

Various methods may reliably identify particular emitters that produceslightly inconsistent emission patterns. Some such methods can reliablyidentify some transmitters with only a single recorded turn-ontransient. In some embodiments, more difficult transmitters withvariable signatures can be reliably fingerprinted by recording severalHistograms of Oriented Gradient (HOG) features.

In some instances, the hardware characteristics of a particular emitter104 may change over time. For example, the turn-on transient of acordless phone may change over the life of the cordless phone. Someembodiments may include signal maintenance modules that update storedsignal features with information corresponding to these physical changesover time. For example, some embodiments may require a user to update,after the lapse of a predetermined amount of time, the HOG features of aparticular emitter 104 stored within database 111.

Although the present disclosure has been described with severalembodiments, a myriad of changes, variations, alterations,transformations, and modifications may be suggested to one skilled inthe art, and it is intended that the present disclosure encompass suchchanges, variations, alterations, transformations, and modifications asfall within the scope of the appended claims.

What is claimed is:
 1. A method for specific emitter identification,comprising: using a processor in performing the steps of: generating acomputer-readable representation of a signal received from an emitter,the received signal being indicative of a hardware characteristic of theemitter; computing a plurality of gradients for each partition of aplurality of partitions of the computer-readable representation, eachgradient indicative of at least the angular orientation of a respectiveportion of the computer-readable representation; for each partition,computing a histogram by assigning each computed gradient to a bin basedat least in part on the magnitude of the computed gradient; extractingone or more Histogram of Oriented Gradient (HOG) features from aconcatenation of the bins of all of the computed histograms; comparingthe one or more HOG features to one or more corresponding HOG featuresstored on a computer-readable medium; and determining, based at least inpart on the comparison, whether the emitter has a particularidentification.
 2. The method of claim 1, wherein the received signalcomprises the turn-on transient of the emitter.
 3. The method of claim1, wherein the generated computer-readable representation of the signalis displayable as a two-dimensional representation of the signal in thetime-frequency domain.
 4. The method of claim 1, wherein computing theplurality of gradients further comprises using a convolution operatorcomprising a Sobel kernel.
 5. The method of claim 1, wherein thecomparing comprises using a K-Nearest-Neighbor (KNN) algorithm.
 6. Themethod of claim 1, further comprising selecting each partition of theplurality of partitions from a set of partitions of thecomputer-readable representation, the selection of each partition basedat least in part on an energy level of the signal represented by thepartition.
 7. The method of claim 1, further comprising normalizing eachcomputed histogram of each partition of the plurality of partitionsusing the computed histogram of at least one other partition of theplurality of partitions.
 8. A specific emitter identification system,comprising: a receiver operable to receive a signal from an emitterindicative of a hardware characteristic of the emitter; a signalprocessor communicatively coupled to the receiver and operable toprocess the signal received from the emitter; a scope communicativelycoupled to the signal processor and operable to generate acomputer-readable representation of the signal processed by the signalprocessor; logic encoded in computer-readable medium and operable whenexecuted to: compute a plurality of gradients for each partition of aplurality of partitions of the computer-readable representation, eachgradient indicative of at least the angular orientation of a respectiveportion of the computer-readable representation; compute a histogram foreach partition by assigning each computed gradient to a bin based atleast in part on the magnitude of the computed gradient; extract one ormore Histogram of Oriented Gradient (HOG) features from a concatenationof the bins of all of the computed histograms; compare the one or moreHOG features to one or more corresponding HOG features stored on acomputer-readable medium; and determine, based at least in part on thecomparison, whether the emitter has a particular identification.
 9. Thesystem of claim 8, wherein the received signal comprises the turn-ontransient of the emitter.
 10. The system of claim 8, wherein thegenerated computer-readable representation of the signal is displayableas a two-dimensional spectrogram of the signal in the time-frequencydomain.
 11. The system of claim 8, wherein the logic is further operableto compute the plurality of gradients using a convolution operatorcomprising a Sobel kernel.
 12. The system of claim 8, wherein thecomparing comprises using a K-Nearest-Neighbor (KNN) algorithm.
 13. Thesystem of claim 8, wherein the logic is further operable to select eachpartition of the plurality of partitions from a set of partitions of thecomputer- readable representation, the selection of each partition basedat least in part on an energy level of the signal represented by thepartition.
 14. The system of claim 8, wherein the logic is furtheroperable to normalize each computed histogram of each partition of theplurality of partitions using the computed histogram of at least oneother partition of the plurality of partitions.
 15. A method forspecific emitter identification, comprising: using a processor inperforming the steps of: generating a computer-readable representationof a signal indicative of a hardware characteristic of an emitter;extracting a plurality of Histograms of Oriented Gradient (HOG) featuresof the computer-readable representation; comparing the one or more HOGfeatures to one or more corresponding HOG features stored on acomputer-readable medium; and determining, based at least in part on thecomparison, whether the emitter has a particular identification.
 16. Themethod of claim 15, wherein the signal comprises the turn-on transientof the emitter.
 17. The method of claim 15, wherein the generatedcomputer-readable representation of the signal is displayable as atwo-dimensional spectrogram of the signal in the time-frequency domain.18. The method of claim 15, further comprising updating one or more ofthe HOG features stored on the computer-readable medium based at leastin part on the extracted plurality of HOG features.
 19. The method ofclaim 15, wherein the comparing comprises using a K-Nearest-Neighbor(KNN) algorithm.
 20. The method of claim 15, wherein the extracting theplurality of HOG features of the computer-readable representationfurther comprises extracting the plurality of HOG features using only asubset, but not all, of the computer-readable representation.